IEEE Solid-State Circuits Magazine - Summer 2015 - 50

applications would need a 1:1 ratio
of ADCs to DACs. In a digitized
telephone call, the analog signal
is captured, transmitted digitally,
then reconstructed back into analog for the listener. However, upon
consideration, we see that a great
many applications have a significant asymmetry: consider the
music on a compact disc or movie
on a DVD-digitized once, then
reconstructed thousands of time
(millions of times, if the recording
is successful).
On the other hand, many digital control systems may monitor
hundreds or thousands of sensors
(each with an ADC) to control two
or three valves (each with a DAC), or
perhaps a digital switch (no conversion required). So, the answer to our
question about commercial significance question is, "it depends." In
practice, the worldwide revenue for
ADCs is roughly three times the revenue of DACs, though this does not
necessarily capture all the embedded converter functionality.

is measured in continuous time.
This means that the ADC is required
to be "right" only once every clock
cycle: it may behave in a completely
nonlinear way at it moves from
one sample to the next, provided
it is accurate by the time the next
sample is taken. For the DAC, on the
other hand, the spectrum analyzer
is always watching: the DAC must
be accurate at each sample point
and-for most applications-be well
behaved (linear) at all times in moving between subsequent samples.
For the DAC's output, there is no
place to hide, and this makes for
some difficult design challenges.
In practice, many signal chains are
ultimately limited by the DAC's performance [40]-[42].

Beyond Bits and Sample Rate
With the dimensions of dynamic range
(bits of resolution) and bandwidth
(sample rate) well established
as the basic measures of performance, we need to introduce some
sort of measure of cost. This will

When monitoring the advance in technology,
one must always factor in both performance
and cost.
In terms of technical difficulty,
the ratio of ADC papers to DAC
papers suggests that the ADC problem is the more interesting one, and,
indeed, intuitively the ADC problem
of "determining the unknown of
where a signal is" is more difficult
than the DAC problem of "faithful reconstruction." But things are
not quite that simple. To defend
the honor of the DAC designer, we
must remind ourselves that the data
converter is moving signals not
just between the analog and digital domains, but between discreteand continuous-time domains. This
means that for most applications,
the ADC's output is judged in discrete time, while the DAC's output

s u m m e r 2 0 15

become the third dimension, and
the denominator in any figure of
merit calculation [8] (see also Boris
Murmann's article in this issue, "The
Race for the Extra Decibel"). Selection of the appropriate cost parameter will again be a function of the
application of concern: it could be
the actual manufacturing cost (for
a consumer application), it could be
physical size or weight (for an application in an aircraft or satellite), or it
could be some other factor.
From a technical perspective, power consumption is often taken as
the third dimension because it has a
strong correlation to size and weight
and-over time at least-tends to have
a good correlation with total system

IEEE SOLID-STATE CIRCUITS MAGAZINE

cost. In many system-on-chip (SOC)
situations, the most important thirddimension consideration is that the
converter be designed on the process
technology required for the remainder
of the system-often a "digital" process. When monitoring the advance in
technology, one must always factor in
both performance and cost.

The applications Universe
Returning to our two dimensions of converter performance-dynamic range
and bandwidth-it can be illuminating
to plot various applications across
a two-dimensional space based on
their converter performance requirements. In this case, we plot
sample rate across the x-axis, and
dynamic range against the y-axis.
Even with a fraction of applications
populated, this performance space
takes shape over some recognizable regions:
■ The "dc" line. At very low sample rates, these applications are
essentially measuring stationary phenomena and may include
instruments like weigh scales,
thermometers, etc. In many cases,
these converters may seek exceptional dynamic range-20 bits or
more-and the need to suppress
errors, such as dc offset and
gain, to realize the best possible
absolute accuracy and stability
over time.
■ Low bandwidth applications,
designed to process signals with
bandwidths of 100 Hz or less.
Many biometric instruments fall
into this performance region,
along with industrial process control and seismic sensors. Dynamic
range requirements can run from
8 bits to 18 bits, depending on the
signal of interest.
■ Audio bandwidth. Reasonable
representations of a human voice
can be realized in 5 KHz of bandwidth (an important consideration for telephony), while high
fidelity audio will utilize bandwidths exceeding 20 KHz. Again,
dynamic range requirements span
a wide range-from eight to 18

Table of Contents for the Digital Edition of IEEE Solid-State Circuits Magazine - Summer 2015